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A214011 T(n,k) is the number of n X n nonnegative integer matrices with row and column i=1..n having sum <= i*k. 10
2, 3, 12, 4, 54, 271, 5, 160, 7722, 24950, 6, 375, 85639, 9318805, 9800058, 7, 756, 564041, 641631566, 98721672541, 16942485560, 8, 1372, 2663506, 17609835599, 69768979161580, 9463992096711104, 131898088386405, 9, 2304, 9976732 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
2, 3, 4, 5, 6;
12, 54, 160, 375, 756;
271, 7722, 85639, 564041, 2663506;
24950, 9318805, 641631566, 17609835599, 269462676001;
9800058, 98721672541, 69768979161580, 11798463876314995, 807203255071567008.
From Robert Israel, Jul 01 2020: (Start)
T(n,k) is the number of integer lattice points in kP where P is an (n^2)-dimensional polytope with vertices having integer coordinates. Therefore row n is an Ehrhart polynomial in k, with degree n^2 and rational coefficients. (End)
LINKS
FORMULA
Empirical: rows 1 2 3 are polynomials of degree 1 4 9.
EXAMPLE
Some solutions for n=3, k=1:
0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0
1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 2
0 0 1 0 0 1 1 2 0 0 0 0 0 1 1 0 0 2 0 0 0
CROSSREFS
Row 2 is A019582(n+2). Rows 3 to 5: A214012, A214013, A214014.
Sequence in context: A046207 A030611 A252177 * A344541 A081369 A147967
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jun 30 2012
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)